The symmetry of the electron-electron interaction operator in the dipole approximation

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Abstract
The operator for the interaction of a charged quantum particle with an excited hydrogen-like atom or ion is considered in the dipole approximation. A new additional integral of motion and related symmetry group are found. A broader approximate symmetry group and expressions for the eigenvalues and eigenfunctions are proposed in the semiclassical limit of large total orbital momentum. The qualitative peculiarities of the spectrum are discussed and limiting cases are considered. A comparison with the results of other authors and with analytical and numerical data is made. The results are applicable to the doubly excited states of two-electron atoms, scattering of charged particles on hydrogen-like atoms or ions, and spectral line broadening etc.

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